flashplayer_32_sa_debug

Please feel free to file bugs over at https://tracker.adobe.com/

That said, the debug versions exist for Flash developers to use to debug their applications.  They're actually much slower than the regular versions, because they're keeping track of a lot of extra information to aid in debugging.  They're not intended for general use (and definitely not general web browsing).

If you want a consistent working experience on Linux, Google Chrome is probably your best bet.  The PPAPI interface abstracts away a lot of the fragmentation between various Linux distributions.  Without knowing the distribution and version you're using, I can't really make a decent recommendation, but it sounds like a permission problem.